Numeric Response
Numeric Response
6. In $\triangle R S T, \angle S=90^{\circ}, \angle R=24^{\circ}$ and $R S=28 \mathrm{~m}$. The length of $R T$, to the nearest tenth is $\mathrm{m}$.
(Record your answer in the numerical-response section below.)
Your answer:

Step 1 ：Given that \(\triangle RST\) is a right triangle with \(\angle S = 90^\circ\) and \(\angle R = 24^\circ\), we can use the trigonometric function sine to find the length of \(RT\). The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, \(\sin(\angle R) = \frac{RS}{RT}\). We can rearrange this equation to solve for \(RT\): \(RT = \frac{RS}{\sin(\angle R)}\).

Step 2 ：Substitute the given values into the equation: \(RS = 28\), \(\angle R = 24\)

Step 3 ：Calculate the value of \(RT\) to get approximately 68.84061339607867

Step 4 ：Round the result to the nearest tenth to get 68.8

Step 5 ：Final Answer: The length of \(RT\), to the nearest tenth, is \(\boxed{68.8}\) meters.